Question: Solve for $x$ and $y$ using substitution. ${-5x+4y = 0}$ ${x = -y+9}$
Solution: Since $x$ has already been solved for, substitute $-y+9$ for $x$ in the first equation. ${-5}{(-y+9)}{+ 4y = 0}$ Simplify and solve for $y$ $5y-45 + 4y = 0$ $9y-45 = 0$ $9y-45{+45} = 0{+45}$ $9y = 45$ $\dfrac{9y}{{9}} = \dfrac{45}{{9}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x = -y+9}\thinspace$ to find $x$ ${x = -}{(5)}{ + 9}$ $x = -5 + 9$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {-5x+4y = 0}\thinspace$ and get the same answer for $x$ : ${-5x + 4}{(5)}{= 0}$ ${x = 4}$